1/2=1-1/2,1/6=1/2-1/3,1/12=1/3-1/4,1/20=1/4-1/5,...1/90=1/9-1/10;
所以原式=1+1-1/2+1/2-1/3+1/3-1/4+1/4-1/5...+1/9-1/10
=1+1-1/10
=19/10